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2016 AMC 10B Problems/Problem 25

Revision as of 09:30, 21 February 2016 by Mathlogin (talk | contribs) (Created page with "==Problem== Let <math>f(x)=\sum_{k=2}^{10}(\lfloor kx \rfloor -k \lfloor x \rfloor)</math>, where <math>\lfloor r \rfloor</math> denotes the greatest integer less than or equ...")
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Problem

Let $f(x)=\sum_{k=2}^{10}(\lfloor kx \rfloor -k \lfloor x \rfloor)$, where $\lfloor r \rfloor$ denotes the greatest integer less than or equal to $r$. How many distinct values does $f(x)$ assume for $x \ge 0$?

$\textbf{(A)}\ 32\qquad\textbf{(B)}\ 36\qquad\textbf{(C)}\ 45\qquad\textbf{(D)}\ 46\qquad\textbf{(E)}\ \text{infinitely many}$

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